Hyundai was building very good cars by that time, and the idea of a luxury Hyundai didn't seem so farfetched to American car shoppers. A 3.5-liter V6 replaced the 3.0-liter engine in the XG300 for 2002, and the XG350 was sold through the 2005 model year, when it was replaced by the Azera.
The 2004 XG350 was priced very reasonably for all the luxury you got, starting at just $23,999 (about $32,350 in 2018 dollars). Compare that to the $39,800 price tag on the most affordable BMW 5-Series that year, or even the $26,040 for a new 2004 Buick LeSabre.
Those cars had more power than the XG350, with its 194-horse V6 driving the front wheels, but it was hard to argue with the car-per-dollar ratio of the big Hyundai.
Sadly, South Korean luxury cars in the United States during the early-to-mid-2000s, from the Daewoo Leganza to the Suzuki Verona, didn't hold their value so well, and many third and fourth owners didn't give them the maintenance they needed. I see lots of these cars in self-service wrecking yards, among all the other South Korean machinery, during my junkyard travels.
In the United States, advertising for the XG was all about suburban virtues and the big factory warranty.
In South Korea, though, the Grandeur's advertising was all about pure schmaltz-drenched luxury.